The author obtains some classification result for the mapping class groups of compact orientable surfaces in terms of measure equivalence. In particular, the mapping class groups of different closed surfaces cannot be measure equivalent.
The author obtains some classification result for the mapping class groups of compact orientable surfaces in terms of measure equivalence. In particul...
The 'measurable Riemann Mapping Theorem' has found a central role in a diverse variety of areas such as holomorphic dynamics, Teichmuller theory, low dimensional topology and geometry, and the planar theory of PDEs. The authors recount aspects of this clas
The 'measurable Riemann Mapping Theorem' has found a central role in a diverse variety of areas such as holomorphic dynamics, Teichmuller theory, low ...
Studies Hardy spaces on $C^1$ and Lipschitz domains in Riemannian manifolds. The author establishes this theorem in any dimension if the domain is $C^1$, in case of a Lipschitz domain the result holds if dim $Mle 3$. The remaining cases for Lipschitz domai
Studies Hardy spaces on $C^1$ and Lipschitz domains in Riemannian manifolds. The author establishes this theorem in any dimension if the domain is $C^...
Studies various subsets of the tracial state space of a unital $C^*$-algebra. This book considers II$_1$-factor representations of a class of $C^*$-algebras by Sorin Popa.
Studies various subsets of the tracial state space of a unital $C^*$-algebra. This book considers II$_1$-factor representations of a class of $C^*$-al...
A memoir dealing with the hypoelliptic calculus on Heisenberg manifolds, including CR and contact manifolds. In this context the main differential operators at stake include the Hormander's sum of squares, the Kohn Laplacian, the horizontal sublaplacian, t
A memoir dealing with the hypoelliptic calculus on Heisenberg manifolds, including CR and contact manifolds. In this context the main differential ope...
This work is an account of the results originating in the work of James and the second author in the 1980s relating the representation theory of GL n(F q) over fields of characteristic coprime to q to the representation theory of quantum GL n at roots of unity. The new treatment allows us to extend the theory in several directions. First, we prove a precise functorial connection between the operations of tensor product in quantum GL n and Harish-Chandra induction in finite GL n. This allows us to obtain a version of the recent Morita theorem of Cline, Parshall and Scott valid in addition...
This work is an account of the results originating in the work of James and the second author in the 1980s relating the representation theory of GL n...
If a black box simple group is known to be isomorphic to a classical group over a field of known characteristic, a Las Vegas algorithm is used to produce an explicit isomorphism. The proof relies on the geometry of the classical groups rather than on difficult group-theoretic background. This algorithm has applications to matrix group questions and to nearly linear time algorithms for permutation groups. In particular, we upgrade all known nearly linear time Monte Carlo permutation group algorithms to nearly linear Las Vegas algorithms when the input group has no composition factor isomorphic...
If a black box simple group is known to be isomorphic to a classical group over a field of known characteristic, a Las Vegas algorithm is used to prod...
The author considers the fundamental lemma for twisted endoscopy, for the units of Hecke algebras only. He proves that it is true if two other lemmas are true - the fundamental lemma for Lie algebras (and non-twisted endoscopy) and another lemma called 'non-standard fundamental lemma'.
The author considers the fundamental lemma for twisted endoscopy, for the units of Hecke algebras only. He proves that it is true if two other lemmas ...
